Tensor Decompositions for Learning Latent Variable Models
Abstract
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models--including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation--which exploits a certain tensor structure in their low-order observable moments (typically, of second- and third-order). Specifically, parameter estimation is reduced to the problem of extracting a certain (orthogonal) decomposition of a symmetric tensor derived from the moments; this decomposition can be viewed as a natural generalization of the singular value decomposition for matrices. Although tensor decompositions are generally intractable to compute, the decomposition of these specially structured tensors can be efficiently obtained by a variety of approaches, including power iterations and maximization approaches (similar to the case of matrices). A detailed analysis of a robust tensor power method is provided, establishing an analogue of Wedin's perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 08, 2012
- Accession Number
- ADA604494
Entities
People
- Anima Anandkumar
- Daniel Hsu
- Matus Telgarsky
- Rong Ge
- Sham Kakade
Organizations
- University of California, Irvine